{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "1777757d",
   "metadata": {
    "_cell_guid": "b1076dfc-b9ad-4769-8c92-a6c4dae69d19",
    "_uuid": "8f2839f25d086af736a60e9eeb907d3b93b6e0e5",
    "execution": {
     "iopub.execute_input": "2022-09-21T07:48:43.530315Z",
     "iopub.status.busy": "2022-09-21T07:48:43.529834Z",
     "iopub.status.idle": "2022-09-21T07:48:44.958766Z",
     "shell.execute_reply": "2022-09-21T07:48:44.957852Z"
    },
    "papermill": {
     "duration": 1.438451,
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     "exception": false,
     "start_time": "2022-09-21T07:48:43.523213",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np \n",
    "import pandas as pd \n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from scipy.optimize import minimize\n",
    "\n",
    "from sklearn.linear_model import Ridge\n",
    "from sklearn.ensemble import BaggingRegressor\n",
    "from sklearn.neural_network import MLPRegressor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c62d3c62",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-21T07:48:44.972297Z",
     "iopub.status.busy": "2022-09-21T07:48:44.971255Z",
     "iopub.status.idle": "2022-09-21T07:48:44.979633Z",
     "shell.execute_reply": "2022-09-21T07:48:44.978004Z"
    },
    "papermill": {
     "duration": 0.015964,
     "end_time": "2022-09-21T07:48:44.982028",
     "exception": false,
     "start_time": "2022-09-21T07:48:44.966064",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "### UTILITY FUNCTIONS TO FIT A LINEAR MODEL WHICH PREDICTS UNCERTAINTY ###\n",
    "\n",
    "def loss(pred_mu, pred_sigma, true):\n",
    "    return np.mean(2*pred_sigma + np.square((true-pred_mu)/np.exp(pred_sigma)))\n",
    "\n",
    "\n",
    "def get_sigma_model(coefs):\n",
    "        \n",
    "    intercept = coefs[-1]\n",
    "    coefs = coefs[:-1]\n",
    "    \n",
    "    sigma_model =  Ridge()\n",
    "    sigma_model.coef_ = coefs\n",
    "    sigma_model.intercept_ = intercept \n",
    "    \n",
    "    return sigma_model\n",
    "    \n",
    "\n",
    "def min_fun(coefs, X, pred_mu, y):\n",
    "    \n",
    "    sigma_model = get_sigma_model(coefs)\n",
    "    pred_sigma = sigma_model.predict(X) \n",
    "    \n",
    "    return loss(pred_mu, pred_sigma, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5c3a3617",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-21T07:48:44.992020Z",
     "iopub.status.busy": "2022-09-21T07:48:44.991055Z",
     "iopub.status.idle": "2022-09-21T07:48:45.006130Z",
     "shell.execute_reply": "2022-09-21T07:48:45.004858Z"
    },
    "papermill": {
     "duration": 0.0226,
     "end_time": "2022-09-21T07:48:45.008628",
     "exception": false,
     "start_time": "2022-09-21T07:48:44.986028",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "### GENERATE SIMULATED DATA ###\n",
    "\n",
    "def sim_data(data, scale=10, return_noise=True):\n",
    "    \n",
    "    stds = (0.15 / (1.0 + np.exp(-data))).clip(0)\n",
    "    noise = np.random.normal(0, stds)\n",
    "    data = (np.sin(data) + noise) *scale\n",
    "    \n",
    "    if return_noise:\n",
    "        return data, noise\n",
    "    return data\n",
    "\n",
    "\n",
    "X_train = np.linspace(-4.0, 4.0, num=1200).reshape((-1, 1))\n",
    "X_test = np.linspace(-7.0, 7.0, num=200).reshape((-1, 1))\n",
    "\n",
    "y_train, _ = sim_data(X_train.ravel())\n",
    "y_test, y_noise = sim_data(X_test.ravel())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b2d3d2f6",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-21T07:48:45.018222Z",
     "iopub.status.busy": "2022-09-21T07:48:45.017702Z",
     "iopub.status.idle": "2022-09-21T07:48:45.819841Z",
     "shell.execute_reply": "2022-09-21T07:48:45.818567Z"
    },
    "papermill": {
     "duration": 0.809849,
     "end_time": "2022-09-21T07:48:45.822309",
     "exception": false,
     "start_time": "2022-09-21T07:48:45.012460",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1152x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### PLOT SIMULATED DATA ###\n",
    "\n",
    "plt.figure(figsize=(16,4))\n",
    "plt.subplot(1,2,1)\n",
    "plt.xlim(X_test.min(), X_test.max())\n",
    "plt.axvspan(X_train.min(), X_train.max(), alpha=0.3, color='orange', label='TRAIN')\n",
    "plt.axvspan(X_train.max(), X_test.max(), alpha=0.3, color='forestgreen', label='TEST')\n",
    "plt.axvspan(X_test.min(), X_train.min(), alpha=0.3, color='forestgreen')\n",
    "plt.scatter(X_test, y_test/10-y_noise, color='black', label='observations')\n",
    "plt.legend()\n",
    "plt.subplot(1,2,2)\n",
    "plt.xlim(X_test.min(), X_test.max())\n",
    "plt.axvspan(X_train.min(), X_train.max(), alpha=0.3, color='orange', label='TRAIN')\n",
    "plt.axvspan(X_train.max(), X_test.max(), alpha=0.3, color='forestgreen', label='TEST')\n",
    "plt.axvspan(X_test.min(), X_train.min(), alpha=0.3, color='forestgreen')\n",
    "plt.scatter(X_test, y_noise, color='black', label='observations')\n",
    "plt.legend()\n",
    "\n",
    "plt.figure(figsize=(16,4))\n",
    "plt.xlim(X_test.min(), X_test.max())\n",
    "plt.axvspan(X_train.min(), X_train.max(), alpha=0.3, color='orange', label='TRAIN')\n",
    "plt.axvspan(X_train.max(), X_test.max(), alpha=0.3, color='forestgreen', label='TEST')\n",
    "plt.axvspan(X_test.min(), X_train.min(), alpha=0.3, color='forestgreen')\n",
    "plt.scatter(X_test, y_test, color='black', label='observations')\n",
    "plt.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d2291013",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-21T07:48:45.834172Z",
     "iopub.status.busy": "2022-09-21T07:48:45.833748Z",
     "iopub.status.idle": "2022-09-21T07:48:45.838782Z",
     "shell.execute_reply": "2022-09-21T07:48:45.837597Z"
    },
    "papermill": {
     "duration": 0.014122,
     "end_time": "2022-09-21T07:48:45.841385",
     "exception": false,
     "start_time": "2022-09-21T07:48:45.827263",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "### DEFINE A BASE MODEL USED TO PREDICT MU ###\n",
    "\n",
    "base_mu_model = MLPRegressor(\n",
    "    max_iter=500, hidden_layer_sizes=(32,32,)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c7594e38",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-21T07:48:45.852963Z",
     "iopub.status.busy": "2022-09-21T07:48:45.852525Z",
     "iopub.status.idle": "2022-09-21T07:48:46.727864Z",
     "shell.execute_reply": "2022-09-21T07:48:46.726208Z"
    },
    "papermill": {
     "duration": 0.886395,
     "end_time": "2022-09-21T07:48:46.732723",
     "exception": false,
     "start_time": "2022-09-21T07:48:45.846328",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "### PREDICT MU ON TRAIN DATA ###\n",
    "\n",
    "mu_model = base_mu_model.fit(X_train,y_train)\n",
    "pred_mu = mu_model.predict(X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2fa60598",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-21T07:48:46.759775Z",
     "iopub.status.busy": "2022-09-21T07:48:46.759013Z",
     "iopub.status.idle": "2022-09-21T07:48:46.790650Z",
     "shell.execute_reply": "2022-09-21T07:48:46.789021Z"
    },
    "papermill": {
     "duration": 0.049945,
     "end_time": "2022-09-21T07:48:46.795181",
     "exception": false,
     "start_time": "2022-09-21T07:48:46.745236",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "### FIT SIGMA MODEL ON TRAIN DATA ###\n",
    "\n",
    "x0_coef = np.ones((2,))\n",
    "res_min = minimize(min_fun, x0_coef, \n",
    "                   args=(X_train, pred_mu, y_train), \n",
    "                   options={'maxiter':10_000})\n",
    "\n",
    "sigma_model = get_sigma_model(res_min.x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "6bd646fa",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-21T07:48:46.822001Z",
     "iopub.status.busy": "2022-09-21T07:48:46.821222Z",
     "iopub.status.idle": "2022-09-21T07:48:47.030496Z",
     "shell.execute_reply": "2022-09-21T07:48:47.029113Z"
    },
    "papermill": {
     "duration": 0.226108,
     "end_time": "2022-09-21T07:48:47.033108",
     "exception": false,
     "start_time": "2022-09-21T07:48:46.807000",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### PLOT SIGMA PREDICTIONS ###\n",
    "\n",
    "pred_sigma1 = np.exp(sigma_model.predict(X_test)) \n",
    "pred_mu = mu_model.predict(X_test)\n",
    "\n",
    "plt.figure(figsize=(8,5))\n",
    "plt.axvspan(X_train.min(), X_train.max(), alpha=0.3, color='orange', label='TRAIN')\n",
    "plt.axvspan(X_train.max(), X_test.max(), alpha=0.3, color='forestgreen', label='TEST')\n",
    "plt.axvspan(X_test.min(), X_train.min(), alpha=0.3, color='forestgreen')\n",
    "plt.xlim(X_test.min(), X_test.max())\n",
    "plt.fill_between(X_test.ravel(), \n",
    "                 pred_mu + pred_sigma1*3, pred_mu - pred_sigma1*3,\n",
    "                 alpha=0.3, color='red', label='std-int')\n",
    "plt.scatter(X_test, y_test, color='black', label='true')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "2e3b9e99",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-21T07:48:47.045752Z",
     "iopub.status.busy": "2022-09-21T07:48:47.045353Z",
     "iopub.status.idle": "2022-09-21T07:48:59.228143Z",
     "shell.execute_reply": "2022-09-21T07:48:59.226857Z"
    },
    "papermill": {
     "duration": 12.193041,
     "end_time": "2022-09-21T07:48:59.231475",
     "exception": false,
     "start_time": "2022-09-21T07:48:47.038434",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "### PREDICT MU ENSEBLES ON TRAIN DATA ###\n",
    "\n",
    "mu_model = BaggingRegressor(\n",
    "    base_mu_model, n_jobs=-1,\n",
    "    max_samples=1., n_estimators=30\n",
    ").fit(X_train,y_train)\n",
    "\n",
    "pred_mu = mu_model.predict(X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "5114ca48",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-21T07:48:59.244236Z",
     "iopub.status.busy": "2022-09-21T07:48:59.243819Z",
     "iopub.status.idle": "2022-09-21T07:48:59.901015Z",
     "shell.execute_reply": "2022-09-21T07:48:59.899243Z"
    },
    "papermill": {
     "duration": 0.668778,
     "end_time": "2022-09-21T07:48:59.905627",
     "exception": false,
     "start_time": "2022-09-21T07:48:59.236849",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "### FIT SIGMA MODELS ON TRAIN DATA ###\n",
    "\n",
    "x0_coef = np.ones((2,))\n",
    "res_min = [\n",
    "    minimize(min_fun, x0_coef, \n",
    "             args=(X_train, m.predict(X_train), y_train), \n",
    "             options={'maxiter':10_000}).x\n",
    "    for m in mu_model.estimators_\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "d5f6738b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-21T07:48:59.933497Z",
     "iopub.status.busy": "2022-09-21T07:48:59.932707Z",
     "iopub.status.idle": "2022-09-21T07:49:00.258115Z",
     "shell.execute_reply": "2022-09-21T07:49:00.256578Z"
    },
    "papermill": {
     "duration": 0.343068,
     "end_time": "2022-09-21T07:49:00.261346",
     "exception": false,
     "start_time": "2022-09-21T07:48:59.918278",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### PLOT SIGMA PREDICTIONS ###\n",
    "\n",
    "pred_vars = np.stack([\n",
    "    np.square(np.exp(get_sigma_model(coef).predict(X_test)))\n",
    "    for coef in res_min\n",
    "], axis=1)\n",
    "\n",
    "pred_mus = np.stack([mu.predict(X_test) for mu in mu_model.estimators_], axis=1)\n",
    "pred_mu = np.mean(pred_mus, axis=1)\n",
    "pred_var = np.mean(pred_vars + np.square(pred_mus), axis=1) - np.square(pred_mu)\n",
    "pred_sigma2 = np.sqrt(pred_var.clip(1e-3))\n",
    "\n",
    "plt.figure(figsize=(8,5))\n",
    "plt.axvspan(X_train.min(), X_train.max(), alpha=0.3, color='orange', label='TRAIN')\n",
    "plt.axvspan(X_train.max(), X_test.max(), alpha=0.3, color='green', label='TEST')\n",
    "plt.axvspan(X_test.min(), X_train.min(), alpha=0.3, color='green')\n",
    "plt.xlim(X_test.min(), X_test.max())\n",
    "plt.fill_between(X_test.ravel(), \n",
    "                 pred_mu + pred_sigma2*3, pred_mu - pred_sigma2*3,\n",
    "                 alpha=0.3, color='blue', label='std-int')\n",
    "plt.scatter(X_test, y_test, color='black', label='true')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "ae5ab679",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-21T07:49:00.275617Z",
     "iopub.status.busy": "2022-09-21T07:49:00.274734Z",
     "iopub.status.idle": "2022-09-21T07:49:00.572941Z",
     "shell.execute_reply": "2022-09-21T07:49:00.571773Z"
    },
    "papermill": {
     "duration": 0.308481,
     "end_time": "2022-09-21T07:49:00.575949",
     "exception": false,
     "start_time": "2022-09-21T07:49:00.267468",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### COMPARE SIGMA INTERVAL WIDTHS ###\n",
    "\n",
    "plt.figure(figsize=(8,5))\n",
    "plt.axvspan(X_train.min(), X_train.max(), alpha=0.3, color='orange', label='TRAIN')\n",
    "plt.axvspan(X_train.max(), X_test.max(), alpha=0.3, color='green', label='TEST')\n",
    "plt.axvspan(X_test.min(), X_train.min(), alpha=0.3, color='green')\n",
    "plt.xlim(X_test.min(), X_test.max())\n",
    "plt.scatter(X_test, pred_sigma1, color='red', label='std-int1')\n",
    "plt.scatter(X_test, pred_sigma2, color='blue', label='std-int2')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  }
 ],
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